Permutation Calculator (nPr)
Calculate the permutation nPr, the number of ordered arrangements of r items chosen from n. Also shows nCr and n factorial.
Input
Enter the total count n and the number to choose r to calculate the permutation nPr, the number of ordered arrangements. The combination nCr and n factorial are shown as well.
Integer of 0 or more
Integer from 0 to n
Result
Permutation nPr choosing r equal to 3 from 5
60
Combination nCr with n equal to 5 and r equal to 3
10
Factorial n with n equal to 5
120
Digits of nPr
2
The permutation nPr equals n factorial divided by (n minus r) factorial, and nCr equals nPr divided by r factorial.
How it works
- A permutation nPr is the number of ways to choose r items from n distinct items and arrange them in order, given by nPr equal to n factorial divided by (n minus r) factorial.
- Equivalently, nPr is the product of r consecutive integers starting at n, that is n times (n minus 1) and so on down to (n minus r plus 1).
- A combination nCr counts selections where order does not matter, given by nCr equal to nPr divided by r factorial.
- When r is 0 both nPr and nCr equal 1, and when r equals n the permutation nPr equals n factorial.
- The inputs must satisfy 0 less than or equal to r less than or equal to n, so r cannot exceed n.
- This tool uses big integer arithmetic, so results stay exact even when the number of digits becomes very large.
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Permutation Calculator (nPr)